Final answer:
The equation for line B is y = (1/3)x + 2, and the equation for line T is y = -3x - 8.
Step-by-step explanation:
To find the equation for line B, we know that it is parallel to line A. When two lines are parallel, they have the same slope. Line A has a slope of 1/3, so line B will also have a slope of 1/3. We can use the point-slope form of a linear equation to find the equation for line B: y - y1 = m(x - x1). Given the point (-3, 1) on line B, the equation for line B is y - 1 = (1/3)(x + 3). Simplifying this equation gives us y = (1/3)x + 2. Therefore, the equation for line B is y = (1/3)x + 2.
To find the equation for line T, we know that it is perpendicular to line A. When two lines are perpendicular, the product of their slopes is -1. Since the slope of line A is 1/3, the slope of line T will be -3. Again using the point-slope form, with the point (-3, 1) on line T, the equation for line T is y - 1 = -3(x + 3). Simplifying this equation gives us y = -3x - 8. Therefore, the equation for line T is y = -3x - 8.